1. Field of the Invention
The present invention relates to a method for modelling the production of hydrocarbons comprising notably relatively high-viscosity oils by petroleum reservoirs subjected to decompression or depletion.
2. Description of the Prior Art
The development of hydrocarbon reservoir production simulation generally involves several stages. Laboratory experiments are first interpreted. Then, the phenomena are modelled on the laboratory scale before an extrapolation is carried out on the reservoir scale. The quantities measurable on the laboratory scale and which have meaning on the reservoir scale therefore have to be determined (saturation, pressure, average concentration). The main requirement lies in the fact that the model must describe, for the same rock-fluids system, with the same parameters, experiments carried out under different conditions, that is for different depletion rate changes, withdrawal rate changes, etc. One of the main parameters is the relative permeability (Kr) which expresses the interactions between the reservoir fluids and the rock (FIG. 1). In water or gas drive methods, the relative permeabilities used for reservoir simulation are directly measured on cores (FIG. 2).
The mechanism of oil production from an underground hydrocarbon reservoir, by means of a decompression (well-known as solution gas drive) has been used and studied for a long time in the petroleum sphere. This production mechanism, which essentially produces oil saturated with light elements by depleting the reservoir, is either favored as in the case of viscous oils or avoided in the case of light oils, at least at reservoir production start, because it leads to an early production of gas and to a low recovery rate. However, in any case, modelling the reservoir production is necessary to control this mechanism.
Modelling of the production by depletion poses a specific problem for numerical simulations. Unlike the water and oil drive production methods, the relative permeabilities Kr measured in the laboratory on samples containing viscous oils cannot be directly used in numerical reservoir simulations. The reason is known and explained in many publications: on the one hand, the diffusion mechanism of the light constituent contained in the oil phase to the gas phase (“off equilibrium” transfer) and, on the other hand, the gas flow in the discontinuous form of bubbles or bubble strings. The consequence of these two effects is that the Kr values determined in the laboratory greatly depend on the experimental conditions, among other things the depletion rate (experiment duration).
Another well-known method of simulating foam flows in a modelled porous medium, known as “Population Balance Modelling”, is described by Arora, P., Kovscek, A. R., 2001, Mechanistic Modeling of Solution Gas Drive in Viscous Oils, SPE 69717 International Thermal Operations and Heavy Oil Symposium, Porlamar, Margarita Island, Venezuela, March 12-14. The method introduces a large number of parameters: nucleation rate, bubble coalescence rate, rate of bubble formation during flow, which cannot be determined experimentally.
Pore network models are also known, which are notably described by Li, X., Yortsos, Y. C., 1991, Visualization and Numerical Studies of Bubble Growth during Pressure Depletion, SPE 22589 66th Annual Technical Conference and Exhibition, Dallas, Tex., October 6-9, based on a pore-scale physics and which therefore cannot simulate an experiment on the scale of a core and take into account of the boundary conditions specific to the experiments. These models have been tested only for light oils and they do not take into account dispersed gas flow.
The model described by Tsimpanogiannis, I. N., Yortsos, Y. C., 2001, An Effective Continuum Model for the Liquid-to-Gas Phase Change in a Porous Medium Driven by Solute Diffusion: I. Constant Pressure Decline Rates, SPE 71502 Annual Technical Conference and Exhibition, New Orleans, La., 30 September-3 October, is a model using continuous equations. It allows good understanding of the mechanisms involved in depletion production (solution gas drive): number of nucleated bubbles, maximum oversaturation, and their influence on the critical gas saturation. On the other hand, it uses a large number of parameters that cannot be directly measured, such as the number and the size of the bubbles. Furthermore, this model does not deal with the flow of the phases and the mass transfer throughout an experiment.
The model described by Sheng, J. J., Foamy Oil Flow in Porous Media, PhD Dissertation, University of Alberta, Edmonton, Canada, takes into account the equilibrium delay due to the growth and to the transfer between a dispersed gas and a continuous gas by means of exponential laws as in a chemical reaction. This method is also used in an industrial simulator (STARS). Such a solution does not show the physics of the phenomenon. It is difficult to interpret experiments in terms of physical parameters and therefore to be predictive. This approach takes into account a dispersed gas phase and a second, continuous phase. Again in this case, transfer between the two phases is governed by a chemical reaction type equation. Calibration is performed by adjusting parameters of the chemical reactions, parameters which are based on no physical justification. It is therefore impossible to predict parameters under reservoir conditions.
In general terms, no known model takes into account, within the scope of the solution gas drive process, and in a continuous approach, all of the mechanisms by allowing calculations under the reservoir flow conditions by using laboratory experiments.